Sweep methods for parallel computational geometry

In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include:

General hidden-surface elimination (even if the overlap relation contains cycles).

CSG boundary evaluation.

Computing the contour of a collection of rectangles.

Hidden-surface elimination for rectangles.

There are interesting subproblems that we solve as a part of each parallelization. For example, we give an optimal parallel method for building a data structure for line-stabbing queries (which, incidentally, improves the sequential complexity of this problem). Our algorithms are for the CREW PRAM, unless otherwise noted.